Question: Simplify the following expression: $q = \dfrac{-20p}{-80p^2 + 130p}$ You can assume $p \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-20p = - (2\cdot2\cdot5 \cdot p)$ The denominator can be factored: $-80p^2 + 130p = - (2\cdot2\cdot2\cdot2\cdot5 \cdot p \cdot p) + (2\cdot5\cdot13 \cdot p)$ The greatest common factor of all the terms is $10p$ Factoring out $10p$ gives us: $q = \dfrac{(10p)(-2)}{(10p)(-8p + 13)}$ Dividing both the numerator and denominator by $10p$ gives: $q = \dfrac{-2}{-8p + 13}$